Questions tagged [least-squares]

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12
votes
2answers
2k views

Newton-based methods in optimization vs. solving systems of nonlinear equations

I asked for clarification about a recent question about minpack, and got the following comment: Any system of equations is equivalent to an optimization problem, which is why Newton-based methods ...
7
votes
2answers
8k views

Least Squares and Fourier Series

I have a little bit of problem figuring out the relation between Fourier series and Least Squares. As far as I understand, LS is a way of minimizing the quadratic error between a measured value $y_i$ ...
11
votes
3answers
1k views

Least squares approximation question

I am taking a course on scientific computation, and we just went over least squares approximation. My question is specifically about approximating using polynomials. I understand that if you have n+1 ...
2
votes
1answer
265 views

Formulation of the least-squares parameter estimation problem

I have a system of 10 ordinary differential equations of the form, $$\frac{dy_1}{dt} = f1(V1,k1,y1,y2)\\ \vdots \\ \frac{dy_{10}}{dt} = f_{10}(V_{10},k_{10},y_{9},y_{10}) $$ I want to estimate the ...
6
votes
3answers
516 views

How to solve a small least-squares problem

This question is not very deep. Suppose I have a small rectangular matrix $A$, with number of rows and columns between $50$-$100$, respectively. Given a right-hand side $b$, I want to solve the least-...
4
votes
1answer
164 views

Factorization for reweighted least squares

I am solving a problem using an iteratively-reweighted least squares method: http://en.wikipedia.org/wiki/Iteratively_reweighted_least_squares Essentially this requires solving a number of least-...
3
votes
0answers
114 views

Backward stable algorithm to get orthogonal projection onto the column space of a matrix

I have to find the orthogonal projection of a vector $b$ onto the matrix $A$ of size $m \times n$. In my application, I don't have the luxury of calculating the QR factorization. All I have are ...
2
votes
1answer
188 views

Solving sparse least squares system with limited memory

This was a question on a past final that we can't figure out. Take the least squares system $$\min_x ||Ax-b||_2\, ,$$ where $A\in\mathbb{R}^{mxn}$, $m<n$, and A is full rank. A has $\mathcal{O}(n)...
1
vote
3answers
363 views

rank-deficient NNLS

I want to find the minimum-norm solution to a rank-deficient least-squares problem, subject to positivity constraints, e.g. $$\min_x\ \|x\|^2 \quad s.t.\quad Ax = b,\ x \geq 0$$ where $A$ is large, ...